11.1.5 Invalid Proofs
If a proof or conclusion contains errors in reasoning, then the conclusion is not valid.
What happens when a conclusion is based on errors in reasoning?
Resources:
Assignment:
- p42 #1, 2, 3, 4, 5, 6, 7, 10
11.1.4 Deductive Reasoning
Deductive reasoning is used to draw conclusions through logic starting with general assumptions that are true.
Resources
- 11.1.4 Notes: Deductive Reasoning
- World's Funniest Joke (Sherlock Holmes)
- Sherlock Holmes Fight Scene
Assignment:
- P.31 #2,4,6,7,8,12,14,17,18*
Consider the two jokes about deductive reasoning:
11.1.3 Counterexamples
Sometimes we make broad, sweeping statements and generalizations that are really conjectures. However, these are the easiest conjectures to prove false. All it takes is one counterexample to prove that a conjecture is false. It is very easy to prove that a conjecture is false, but using inductive reasoning, it is very difficult to prove that a conjecture is true.
Resources:
Assignment:
- p22 #1, 4, 5, 11, 12, 16, 17
11.1.2 Conjecture Validity
Sometimes we may consider a number of possible conjectures. How do we know which ones may be valid? We can ask questions that test whether a conjecture may still be valid or correct.
Resources:
- Notes: Testing Conjectures
- Worksheet: Conjecture Validity ( you will need to obtain one of the handouts in class that has 2 crime puzzles)
Assignment:
- Worksheet
- "Math in Action" on p15
- p17 #1, 2, 3
Additional Resources: